Month April May June July Machine Hours Worked 5650 5200 750

Month April May June July Machine Hours Worked 5,650 5,200 7,500 9,000 Utilities Cost 10,060 9,940 11,725 13,400 Lichtenstein anticipates producing 6,000 units in August, each unit requiring 2.5 hours of machine time. The company uses the high- low method to analyze costs Required A. Calculate the variable and fixed components of the utilities cost. B. Using the data calculated above, estimate the utilities cost for August. For all requirements, round \"variable cost per hour\" to 2 decimal places and final answers to the nearest dollar amount. A. Variable cost per hour Fixed cost B. Total variable cost Total fixed cost Total utilities cost for August

Solution

High-Low method is one of the several techniques used to split a mixed cost into its fixed and variable components. These figures are then used to calculate the approximate variable cost per unit (b) and total fixed cost (a) to obtain a cost volume formula:

y = a + bx

High-Low Method Formulas:

Variable Cost per Unit:

Variable cost per unit (b) is calculated using the following formula:

Variable Cost per Unit= y₂ ? y₁

                                        x₂ ? x₁

Where,
y₂ is the total cost at highest level of activity;
y₁ is the total cost at lowest level of activity;
x₂ are the number of units/labor hours etc. at highest level of activity; and
x₁ are the number of units/labor hours etc. at lowest level of activity

The variable cost per unit is equal to the slope of the cost volume line (i.e. change in total cost ÷ change in number of units produced).

The volume and the corresponding total cost information of the factory for past four months are given below:

Month

Machine Hours worked

Utilities cost

April   

5,650

$10,060

May

5,200

9,940

June

7,500

11,725

July

9,000

13,400

Solution:

We have,
at highest activity: x₂ = 9,000; y₂ = $13,400
at lowest activity: x₁ = 5,200; y₁ = $9,940

Variable Cost per Unit = ($13,400 ? $9,940) ÷ (9,000 ? 5,200) = $0.91 per unit

Total Fixed Cost:

Total fixed cost(a) is calculated by substracting total varible cost from total cost, thus:

Total fixed cost = y₂ ? bx₂ = y₁ ? bx₁

Total Fixed Cost = $13,400 ? ($0.91 × 9,000) = $9,940 ? ($0.91 × 5,200) = $5,210
Cost Volume Formula: y = $5,210 + 0.91x

Final Answer: for producing 6,000 units in the month of Auguest

Fixed cost                 = $ 5,210

                                 = (6,000*2.5) * 0.91

                                 = 15,000*0.91

                                 = $ 13,650

Total fixed cost        = $ 5,210 (never changed based on production)

Total utilities cost for Auguest= 13,650+5,210 = $ 18,860

Month	Machine Hours worked	Utilities cost
April	5,650	$10,060
May	5,200	9,940
June	7,500	11,725
July	9,000	13,400